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Article Growth and Yield Models for Balsa in the Coastal Lowlands of Ecuador

Álvaro Cañadas-López 1,2, Diana Rade-Loor 3, Marianna Siegmund-Schultze 4, Geovanny Moreira-Muñoz 1, J. Jesús Vargas-Hernández 5 and Christian Wehenkel 6,* 1 Carrera Ingeniería Agropecuaria, Facultad de Ingeniería Agropecuaria, Universidad Laica Eloy Alfaro de Manabí, C.P.130301 Av. Eloy Alfaro, Chone, Ecuador 2 Programa de Forestaría, Instituto Nacional de Investigaciones Agropecuarias (INIAP), Estación Experimental Tropical Pichilingue, C.P. 120501 Km 5 vía Quevedo—El Empalme, Pichilingue, Ecuador 3 Centro de Investigación de las Carreras de la ESPAM-MFL (CICEM), Escuela Superior Politécnica de Manabí (ESPAM-MFL), Campus Politécnico Calceta, C.P. 130250 Sitio El Limón, Calceta, Ecuador 4 Environmental Assessment and Planning Research Group, Technische Universität Berlin, Straße des 17. Juni 145, 10623 Berlin, Germany 5 Posgrado en Ciencias Forestales, Colegio de Postgraduados, Montecillo, Texcoco C.P. 56230, México 6 Instituto de Silvicultura e Industria de la Madera, Universidad Juárez del Estado de Durango, Boulevard Guadiana #501, Ciudad Universitaria, Torre de Investigación, Durango C.P. 34120, México * Correspondence: [email protected]

 Received: 2 July 2019; Accepted: 20 August 2019; Published: 26 August 2019 

Abstract: Balsa are native to neotropical and frequently grow on fallow, degraded land. Balsa can be used for economic and ecological rehabilitation of farmland with the aim of restoring native ecosystems. Although Ecuador is the world’s largest producer of balsa, there is a lack of knowledge about production indicators for management of balsa stands in the country. The aim of this study was to develop growth and yield models (i.e., (SI) curves and stem volume models) for balsa plantations in the coastal lowlands of Ecuador. Balsa trees growing in 2161 plots in seven provinces were sampled. Here we present the first growth and yield models for the native, although underutilized, balsa . Three curve models were fitted to determine SI for balsa stands, differentiating five site quality classes. Eight volume models were compared to identify the best fit model for balsa stands. The mean annual increment was used to assess balsa production. The generalized algebraic difference approach (GADA) equation yielded one of the best results for the height–age and diameter–age models. The Newnham model was the best volume model for balsa in this comparative study. The maximum annual increment (i.e., for the best stand index) was reached in the second year of . The fitted models can be used to support management decisions regarding balsa plantations. However, the models are preliminary and must be validated with independent samples. Nevertheless, the very fast development of the native balsa tree is particularly promising and should attract more attention from forest owners and politicians.

Keywords: mean annual increment; stand density index; site index; silvicultural models; volume; native tree; underutilized tree

1. Introduction Many non-native tree species have been used around the world for productive plantations, ornamental purposes and for rehabilitation of degraded land, eventually contributing to the homogenization of landscapes, reducing native diversity, and with mixed effects on ecosystem services [1]. Rehabilitation of degraded land is a worldwide necessity and is increasingly gaining political attention. In the context of climate change and biodiversity loss, locally-adapted solutions

Forests 2019, 10, 733; doi:10.3390/f10090733 www.mdpi.com/journal/forests Forests 2019, 10, 733 2 of 16 are needed. The balsa tree, Ochroma pyramidale (Cav. Ex Lam), is native to the neotropical forests and frequently grows on fallow and degraded land. It can be used for economic, ecological rehabilitation of farmland with the aim of restoring native forest ecosystems [2,3]. In 2008, Ecuador was the world’s top producer of balsa wood, producing 89% of the balsa sold worldwide, followed by Papua New Guinea with 8%. The global trade in sawn kiln-dried balsa wood and semi-finished wood products (155,000 m3) was worth an estimated US $71 million [4]. According to Cañadas [5], the economic value of potential forestlands could be increased by using light-demanding trees such as balsa to establish plantations and systems. Balsa has considerable potential in secondary forests and on abandoned agricultural land: It grows rapidly, the wood quality meets the requirements of the industry, and the species appears suitable for plantations and agroforestry systems. It could meet increased future requirements of the industry, as production costs are low [6,7]. Balsa is known as a “frame species” because of the following properties: (1) Good survival and high growth rates in degraded conditions; (2) rapid canopy development, which suppresses highly competitive heliophilous weeds; and (3) it provides food and perches that attract seed dispersal fauna [8]. These characteristics are associated with improved soil fertility [9], rehabilitation of degraded areas, and [2]. Balsa plantations are deemed an economic alternative for the Ecuadorian coastal region because of the very light wood and versatility for adaptation to the needs of local small producers and timber exportation [10]. These characteristics contribute to the diversification of production in smallholder farming systems [11]. The main components that influence the quality of plantation sites are climate and soil. In forest studies, site quality has been evaluated with the help of different indices. In even-aged stands, site index (SI) is the most popular means of assessing site quality and is also used to evaluate tree growth and yield potential. SI relates tree height or diameter of a species to tree age. However, SI and height growth are sensitive to incidents in the stand history [12,13]. Finally, measuring volume production of trees is a difficult task, and easier methods are desirable [14–17]. In 2016, the Ecuadorian Forest Incentives Program (PROFORESTAL), implemented by the Ministry of Agriculture, Livestock, and Aquaculture (MAGAP), recorded a total of 48,533 ha of forest plantations with the following species: ( grandis L.), 19,602 ha; melina (Gmelina arborea Roxb.), 10,467 ha; balsa, 8518 ha; , 4733 ha; and other species, in the remaining 5213 ha [18]. Growth models predicting balsa stand development would be useful to estimate the stand dynamics and thus sustain decision making in stand management. Nevertheless, management of balsa stands suffers from a lack of reliable quantitative for simulating stand dynamics [19]. In addition, little research has addressed production, silvicultural, and management aspects of balsa, such as SI, stand density, growth rate, and soil fertility [19], except for a previous study in which we modelled the SI of Ecuadorian balsa for both height and diameter on the basis of the Chapman-Richards model [7]. However, there are wide array of growth and yield models, each with advantages and disadvantages. These models differ in the type of data used and the method of construction [20]. The aim of this study was to develop the first growth and yield models, including SI curves and volume models, for balsa plantations in the coastal region of Ecuador, thus contributing to the development of further silvicultural and economic studies.

2. Materials and Methods

2.1. Study Area Balsa plantations were evaluated in seven provinces in the coastal region of Ecuador (Figure1). Forests 2019, 10, 733 3 of 16 Forests 2019, 10, x FOR PEER REVIEW 3 of 16

Figure 1. Spatial distribution of the balsa sampling plots in the coastal lowland provinces in Ecuador. Figure 1. Spatial distribution of the balsa sampling plots in the coastal lowland provinces in Ecuador. The climate data for the period 2009–2013 was taken from the Instituto Nacional de Meteorología The climate data for the period 2009–2013 was taken from the Instituto Nacional de Meteorología e Hidrología (INAMHI) [21] meteorological yearbook. The number of plots sampled in each site was e Hidrología (INAMHI) [21] meteorological yearbook. The number of plots sampled in each site was proportional to the surface area of each Balsa plantation. Table1 shows the basic stand attributes of proportional to the surface area of each Balsa plantation. Table 1 shows the basic stand attributes of balsa plantations in the research region. Table2 summarizes the annual precipitation, mean annual balsa plantations in the research region. Table 2 summarizes the annual precipitation, mean annual temperature, elevation, and the number of plots sampled by province and life zone, defined as temperature, elevation, and the number of plots sampled by province and life zone, defined as evapotranspiration potential. evapotranspiration potential.

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Table 1. Mean stand characteristics of the Balsa plantations by province in the coastal region of Ecuador.

Density of Diameter at Total Mean Annual Basal Area Province Plantation Age (Year) Breast Height Height 2 1 Increment * 1 (m ha− ) 3 1 (Trees ha− ) (cm) (m) (m ha− ) Average 334.4 4.4 22.4 22.4 13.0 29.2 Maximum 1506.0 10.9 44.1 40.6 26.0 228.1 Los Ríos Minimum 90.0 1.1 2.9 2.5 0.3 2.2 Stand Err 712.5 0.1 1.1 1.3 0.6 5.1 ± ± ± ± ± ± Average 343.2 4.1 22.5 22.7 14.1 33.0 Santo Domingo Maximum 856.0 9.4 44.6 35.0 26.9 198.4 de los Tsáchilas Minimum 100.0 1.3 3.8 7.4 2.0 2.3 Stand Err 777.4 0.1 1.4 1.6 0.8 9.9 ± ± ± ± ± ± Average 390.5 3.9 23.3 23.9 15.8 39.2 Maximum 760.0 7.2 37.5 34.6 28.1 99.5 Cotopaxi Minimum 190.0 1.5 8.8 10.7 4.8 10.4 Stand Err 892.2 0.2 2.8 2.9 1.8 15.3 ± ± ± ± ± ± Average 280.7 5.1 21.9 23.1 11.6 22.9 Maximum 800.0 10.8 35.2 34.3 22.5 43.9 Manabí Minimum 90.0 1.4 6.8 7.4 2.2 3.0 Stand Err 280.7 0.6 3.8 4.9 1.7 6.4 ± ± ± ± ± ± Average 408.5 3.6 19.2 20.6 11.9 29.4 Maximum 599.0 6.8 33.6 28.6 22.0 52.1 Guayas Minimum 194.0 1.8 10.9 10.8 4.6 7.1 Stand Err 881.9 0.2 4.2 3.4 2.3 13.4 ± ± ± ± ± ± Average 361.4 3.8 21.8 20.5 13.4 16.3 Maximum 569.0 6.5 32.5 27.8 30.0 38.9 Esmeraldas Minimum 155.0 1.5 13.7 11.4 6.0 18.3 Stand Err 2842.5 0.3 4.2 4.2 4.9 28.4 ± ± ± ± ± ± Average 337.0 3.9 24.6 20.2 11.6 23.1 Maximum 493.0 6.8 32.6 27.6 19.2 37.4 Pichincha Minimum 210.0 1.8 15.3 9.9 4.0 7.4 Stand Err 1160.5 0.6 5.9 5.7 3.3 9.8 ± ± ± ± ± ± * Note: Mean annual increment is the total growth of a stand up to a given age divided by the total age.

Table 2. Province, general conditions, and number of plots in the balsa plantations under study in the coastal region of Ecuador.

Total Annual Mean Annual Elevation Number of Province Precipitation Temperature (Meters above Life Zone * Plots (mm) (◦C) Sea Level) Los Ríos 2000 25.2 30–300 1300 TwF-TrF Santo Domingo 2280 23.5 200–700 529 Twf-TrF de los Tsáchilas Cotopaxi 3019 24.0 300–600 117 TmF-TrF Manabí 1000 24.6 20–300 100 TdF-TrF Guayas 1189 26.7 30–100 56 TdF-TrF Esmeraldas 2646 25.6 100–300 32 TwF-TrF Pichincha 1998 25.0 300–700 27 TwF-TrF * According to Cañadas [5]: Tropical dry forest, evapotranspiration potential 1–2 (TdF); tropical moist forest, evapotranspiration potential 0.5–1 (TmF); tropical wet forest, evapotranspiration potential 0.2–0.5 (TwF); tropical rain forest, evapotranspiration potential 0.1–2 (TrF).

2.2. Data Collection The data was collected from a total of 2161 plots. Due to the planting density (Table1), the sampled plot sizes varied from 500 to 5000 m2 to yield a minimum of 40 balsa trees per plot. Each rectangular plot was georeferenced and coded, and the plantation age was recorded after consulting the plantation owner. Diameter at breast height (DBH) was measured with a caliper. The height (H) was estimated with a Haga hypsometer. Two consecutive measurements (2015–2016) were made. Forests 2019, 10, 733 5 of 16

2.3. Site Index Assessment

Mean dominant height (Hd) and diameter at breast height (DBHd) were estimated as mean values for each sample plot of the 30 tallest balsa trees. In this study, different asymptotic models were applied to the height–age and diameter–age data to determine the best fitting model. Three different models were used to assess the SI: The model equations developed by Chapman-Richards [22] (Equation (1)), Hossfeld II cited in Peschel [23] (Equation (2)), and the generalized algebraic difference approach (GADA) (Equations (3) and (4)) [24]. All were computed in R software (version 3.3.3) (R foundation for Statistical Computing, Vienna, Austria).

( bt) c H = a(1 e − ) (1) d − 2 t(a1 + a2t ) H = (2) d 3 a3 + t where Hd = dominant height (m); t = age (year); a1, a2, a3 = equation parameters. Polymorphic curves were developed from these curves, using the maximum height reached at 5 years of age as the reference [25] in this study. The guide curves obtained by Equations (1) and (2) were compared with the generalized algebraic difference approach (GADA) [26,27]. Owing to its flexibility, the three-parameter Chapman–Richards model is widely used in forest growth modelling and prediction, especially for developing site index models [28,29]. Parameter a1 is the maximum value of this growth variable. a2 is an empirical growth parameter scaling the absolute growth rate. The empirical parameter a3 is related to catabolism rate [30]. The starting point of the curve is at the origin of , which is only useful if growth begins at zero [31]. The Hossfeld equation generates S-shaped curves giving a realistic growth of young trees and generates sensible curves when extrapolating outside the age and SI range of the data [32]. The advantage of GADA over guide curves and the algebraic difference approach (ADA) is that it produces dynamic site equations that are base-age-invariant (BAI) and have the path invariance property (PIP). GADA; thus, allows more than one parameter to be site specific. GADA site curves display “concurrent” polymorphism and variable asymptotes and use a variety of growth characteristics that operate across different sites [33]. For application of the GADA method, Equation (1) (Chapman-Richards) was selected to identify which parameters depended on site productivity. Thus, the selected parameters are expressed as site quality functions via the variable X0.X0 is an unobservable, independent variable that describes site productivity and reflects the management and ecological conditions and new parameters. The bi-dimensional equations (H = f (t)) were expanded to three-dimensional equations of the site index (Hd = f (t, X)), determining X from the initial site conditions (t0 and H0)[26]. The polymorphic curves with multiple asymptotes can be obtained by the GADA method with the following dynamic equation (Equation (3)). " b t #(b2+b3/Xo) 1 e− 1 1 H1 = − (3) 1 e b1to − − where H0 is the dominant height at the initial age, t0 and H1 is the dominant height at age t1. H0 is derived for Equation (4). ( q ) 1 X = ln H b L [ln H b ]2 4b L (4) 0 2 0 − 2 0 ± 0 − 2 − 3 0 where L = ln[1 exp b t ]. Fitting this equation with the dominant height–age data enables estimation 0 − − 1 0 of the values of the global parameters b1, b2, b3. The family of curves obtained by the GADA method are invariant relative to the reference age and invariant relative to the simulation path [27,34]. The mean structure (determined with the growth equation) and the mean error structure (determined by the auto regression model) were fitted simultaneously with the GADA package, in R (version 2.2.2) (R Foundation Forests 2019, 10, 733 6 of 16 for Statistical Computing, Vienna, Austria [35] (Development Core Team 2018). The procedure was also applied to DBHd in order to generate the three-mean dominant DBH–age models (Equations (1)–(4)). Fitting the performance of the Hd and DBHd models was based on comparison of curves. The bias and the root mean errors (RMSEs) were calculated from the residuals obtained during the fitting stages. Graphical analysis was carried out by (1) superimposing the fitted curves, (2) plotting residuals against the values predicted by the model, and (3) analyzing changes in bias and RMSEs for the different age groups.

2.4. Tree Volume Assessment A total of 532 dominant balsa trees (diameter average 23.1 0.5 cm, height average 15.5 0.6 m) ± ± were selected and destructively sampled in seven provinces with a total of 76 trees per province. The DBH and H were measured before and after the trees, respectively. A diameter tape was used to measure the diameter (di) over the bark on the ground and at different heights: 0.3 m, 2.3 m, and every 2.0 m along the stem to the top. The total tree volume of each tree (V, m3) was calculated by measuring the diameter at each end of the section (di and di+1) and the length of sections (l) of the felled specimens using the following formula [16]:

 2 2 1π d (didi+1) di+  V = ( i ) + + ( 1 )  (5) 3  2 4 2 

Several commonly-used volume estimation models [36] were tested to determine the best regression model for V, DBH, and H for the balsa stands (Table3). The parameters to be determined are a, b, c, and d. The generalized method of moments (GMM), implemented in SAS/ETS® [37], was used to fit the models.

Table 3. Models tested for fitting volume equations for balsa trees by using diameter at breast height (DBH in cm) and total tree height (H in m) of dominant trees.

Model Expression Schumacher-Hall (allometric) [38] V = a DBHb Hc (6) × × Spurr [39] V = a DBH2 H (7) × × Spurr potential [40] V = a (DBH H)b (8) × × Spurr with independent term [40] V = a + b DBH2 H (9) × × Incomplete generalized combined variable [40] V = a + b H + c DBH2 H (10) × × × Australian formula [41] V = a + b DBH2 + c H + d DBH2 H (11) × × × × Honer [42] V = DBH2/(a + b/H) (12) Newnham [43] V = a + b DBHc Hd) (13) · ×

We estimated the goodness of fit of the volume models from the mean squared error (MSE), 2 standard error (SE), and adjusted determination coefficient (R Adj). Finally, the best model (of those tested) was selected by the Akaike information criterion (AIC), where lower AIC values indicate better performance [44]. Use of AIC or other criterions, such as the Bayesian information criterion, are a way of selecting the model that best balances (i) the true nature of the variability in the outcome variable and (ii) model generality [45].

2.5. Assessment of Balsa Production

1 The average density of the balsa stands in the study region was 300 trees ha− . The total volume was estimated by the modelled mean tree volume per age and SI multiplied by the indicated stand density. Mean annual increment (MAI) and periodic annual increment (PAI) were calculated. MAI is the total growth of a tree or stand up to a given age divided by the total age. PAI is equal to the tangent slope to the growth curve and describes the growth rate at age t. The PAI is cumulated at maximum tangent slope, where the tangent and the growth curve pass through the origin [46]. Forests 2019, 10, 733 7 of 16

3. Results

3.1. Balsa Site Index The estimated parameters for Equations (1)–(3), and the fitting statistics are shown in Table4. All parameters were significant at the 1% level, including the site-dependent parameter for each tree. The lowest values of RMSE corresponded to the GADA method, for both Hd and DBHd.

Table 4. Estimated values of parameters, p values, and goodness-of-fit statistics for the three-mean height–age and diameter–age models for balsa plantations of the coastal region of Ecuador.

Estimated Standard Parameter Model Parameter p Value RMSE Value Error

a1 31.844 0.6646 <0.001 Equation (1) a2 0.2973 0.0247 <0.001 13.79 a3 1.0767 0.0662 <0.001

a1 0.8036 0.0065 <0.001 Height–Age Equation (2) a 0.1382 0.0001 <0.001 6.43 2 − a3 0.1331 0.001 <0.001

b1 0.4207 0.1483 <0.001 Equation (3) b 4.6136 0.2719 <0.001 4.27 2 − b3 20.395 5.4538 <0.001

a1 33.607 0.7364 <0.001 Equation (1) a2 0.3108 0.0372 <0.001 23.06 a3 0.7876 0.0696 <0.001

a1 1.3090 0.00003 <0.0000001 Diameter–Age Equation (2) a 0.1886 0.00001 <0.001 8.53 2 − a3 0.1792 0.00004 <0.0000001

b1 0.7989 0.0791 <0.0000001 Equation (3) b 9.7819 2.3562 <0.0000001 5.61 2 − b3 41.234 0.2583 <0.0000001

Figure2 shows the results of analysis of the bias and RMSE evaluation for the age classes for both Hd and DBHd. Estimation with the GADA method showed a distribution of bias around zero for both parameters with no consistent trend. For RMSE, both Chapman-Richards and Hossfeld equations exhibited a similar trajectory for all age classes. The Chapman-Richards and GADA model showed a low RMSE, especially for the juvenile ages, for Hd. The largest bias and RMSE dispersions were particularly observed in the age class 9 to 10 years due to the lack of data for these classes. The GADA method; thus, yielded good fit models. Forests 2019, 10, 733 8 of 16 Forests 2019, 10, x FOR PEER REVIEW 8 of 16

A B

15 15 Richard Hossfeld Gada Richard Hossfeld GADA

10 10

5 5 Bias (cm)

Bias (m) 0 0 012345678910 012345678910

-5 -5

-10 Age (year) -10 Age (year) D C

16 16 Richard Hossfeld Gada Richard Hossfeld GADA 14 14

12 12

10 10

8 8 RMSE (m)RMSE 6

RSME (cm) 6

4 4

2 2

0 0 012345678910 012345678910 Age (year) Age (year)

FigureFigure 2.2. BiasBias ((AA,,BB)) andand rootroot meanmean squaresquare errorerror (RMSE;(RMSE; CC,,DD)) byby ageage classclass forfor dominantdominant heightheight ((HHdd) ((AA,C,C)) andand dominantdominant diameterdiameter atat breastbreast heightheight ((DBHDBHdd)() (B,,D)) estimatedestimated withwith thethe EquationsEquations (1)–(3)(1)–(3) (Chapman-Richards,(Chapman-Richards, Hossfeld,Hossfeld, GADAGADA formulation,formulation, respectively).respectively).

WithWith thethe GADAGADA procedureprocedure basedbased onon thethe Chapman-RichardsChapman-Richards basebase model,model, bothboth parametersparametersa a11 andand aa33 are dependent on-site quality and the error structurestructure isis includedincluded inin thethe interactioninteraction procedure:procedure:

(−+ 4.6136 20.3953/X ) " −×0.42017#t( 4.6136+20.3953/X00) 1 1e −0.42017e t1 1− HeightH = =H − − × (14) Height—d1HHdd10d0 0.42017−×t (14) 1 e− 0.420170 t0 −1− e × " #( 9.7919+41.2342/X ) 0.7989 t1 0 1 e− × − −+ −×( 9.7919 41.2342/X0 ) DiameterDBHd1 = DBHd0 − 0.7989 t1 (15) 1−0.7989e t0 = 1 e− × (15) Diameter— DBHdd10 DBH − −× − 0.7989 t0 where H1 is the predicted height (m) at age t1 (years),1 ande H0 and t0 represent the initial dominant height and age. where H1 is the predicted height (m) at age t1 (years), and H0 and t0 represent the initial dominant Height height and age. ( q ) 1 2 Height X0 = ln H0 4.6136 L0 [ln H0 4.6136] 81.5812 L0 2 − × ± − − × (16) h ( 4.6136 t )i 1 L0 = ln 1 e − × 0 2 X =−×±−−×{lnHLH 4.6136−[] ln 4.6136 81.5812 L} 00 00 0 Diameter 2 (16)

( q (.×) ) 1 𝐿 =𝑙𝑛1−𝑒 2 X0 = ln H0 9.7819 L0 [ln H0 9.7819] 164.9379 L0 2 − × ± − − × (17) Diameter h i L = ln 1 e( 9.7819 t0) 0 − − × =−×±−−1 []2 × BalsaX site00 index{ln wasHLH divided 9.7819 into five classes.00 ln Class one 9.7819 (I) represented 164.9379 the best site L 0 quality} and 2 (17) class V the poorest quality both for H and DBH. The GADA model was used to fit SI curves for Hd (.×) (from 34.6 to 15.3 m) and DBHd (from𝐿 40.3 =𝑙𝑛1−𝑒 to 15.6 cm) at a reference age of five years. The fitted curves follow the same trends. The curves did not perform better for any particular province (Figure3). Balsa site index was divided into five classes. Class one (I) represented the best site quality and class V the poorest quality both for H and DBH. The GADA model was used to fit SI curves for Hd (from 34.6 to 15.3 m) and DBHd (from 40.3 to 15.6 cm) at a reference age of five years. The fitted curves follow the same trends. The curves did not perform better for any particular province (Figure 3).

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45 45 40 40 35 35 30 30 25 25 Total height (m) Total height 20 20

15 15

10 Diameterat breast height (cm) 10

5 5 0 0 012345678910 012345678910 Age (year) Age (year) COTOPAXI ESMERALDAS COTOPAXI ESMERALDAS GUAYAS LOS RIOS GUAYAS LOS RIOS PICHINCHA SANTO DOMINGO DE LOS TSACHILAS PICHINCHA SANTO DOMINGO DE LOS TSACHILAS MANABI MANABI

(a) (b)

FigureFigure 3. Site 3. indexSite index curves curves for forfive five site site class class for for balsa balsa in in the coastal lowlandslowlands of of Ecuador. Ecuador. (a) ( Totala) Total heightheight (14, 19, (14, 24, 19, 29, 24, and 29, and34 m) 34 m)and and (b) ( bdiameter) diameter at at breast breast height height (20, 25,25, 30, 30, 35, 35, and and 40 40 cm), cm), using using the the GADAGADA model model (for (for a reference a reference age age of of five five years). years). 3.2. Volume Models 3.2. Volume Models The outcome of the fitted regression of the eight-volume function estimation for balsa is given in TheTable outcome5. of the fitted regression of the eight-volume function estimation for balsa is given in Table 5. Table 5. Goodness of fit statistics of the models predicting the volume (in m3 for diameter at breast height over bark of 5 cm or more) of balsa plantations in the coastal lowlands of Ecuador. Table 5. Goodness of fit statistics of the models predicting the volume (in m3 for diameter at breast 2 height over Modelbark of 5 cm or more) MSE of balsaR Adj plantationsParameter in the coastal Estimator lowlands of SEEcuador. AIC a 0.349727 0.0198 Model MSE R2 Adj Parameter Estimator SE AIC b 0.000024 0.000005 Newnham 0.028 0.909 392 c a 2.3431510.349727 0.0629 0.0198− d b 0.7604810.000024 0.0518 0.000005 Newnham 0.028 0.909 −392 Spurr with a 0.322645 0.0124 0.028 0.907 c 2.343151 0.0629380 independent term b d 0.0000420.760481 0.0000003 0.0518− Incomplete a a 0.2792410.322645 0.0528 0.0124 Spurr withgeneralized independent combined term0.028 0.028 0.907 0.907 b 0.00375 0.00379 379 −380 − variable c b 0.0000410.000042 0.0000008 0.0000003 a 0.279241 0.0528 Incomplete generalized combined a 0.282614 0.0572 b 0.00006 0.000050 Australiana formula 0.0280.028 0.907 0.907 b − 0.00375 0.00379378 −379 variable c 0.004089 0.00382 c 0.000041 0.0000008− d 0.000043 0.000002 a 0.282614 0.0572 a 0.002402 0.000331 Schumacher-Hall 0.046 0.849 b b 1.100958−0.00006 0.0465 0.000050122 Australiana(allometric) formula 0.028 0.907 − −378 c c 0.8192850.004089 0.0738 0.00382 a 0.002264 0.000281 Spurr potential 0.046 0.848 d 0.000043 0.000002121 b 0.980555 0.0181 − a 0.002402 0.000331 a 973.3571 38.4457 Honer 0.058 0.809 1.56 Schumacher-Hall (allometric) 0.046 0.849 b b 1995.991.100958 822.1 0.0465 −122 − Spurr 0.081 0.733 a c 0.0000550.819285 0.0000004 0.0738 177 MSE = mean squared error; R2 = adjusted determination coeffia cient; SE = 0.002264standard error; AIC0.000281= Akaike Spurr potential Adj 0.046 0.848 −121 information criterion. b 0.980555 0.0181 a 973.3571 38.4457 HalfHoner of the tested models provided0.058 good0.809 fits to the data with an adjusted R2 > 0.9. For the1.56 b −1995.99 822.1 Newnham, Spurr with independent term, incomplete generalized combined variable, and Australian formula models,Spurr the adjusted R2 values0.081 were 0.733 0.9. According a to the AIC0.000055 criterion, the0.0000004 model that best177 MSE = mean squared error; R2Adj = adjusted determination coefficient; SE = standard error; AIC = Akaike information criterion.

Half of the tested models provided good fits to the data with an adjusted R2 > 0.9. For the Newnham, Spurr with independent term, incomplete generalized combined variable, and Australian formula models, the adjusted R2 values were 0.9. According to the AIC criterion, the model that best

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fits the characteristics of the balsa tree stands was the Newnham model (Equation (13)). However, fits the characteristics of the balsa tree stands was the Newnham model (Equation (13)). However, this this model overestimates the volume of trees with a DBH under 15 cm. model overestimates the volume of trees with a DBH under 15 cm. 3.3. Mean Annual Increment 3.3. Mean Annual Increment The optimal biological rotation was obtained for each SI at a reference age (Figure 4). The The optimal biological rotation was obtained for each SI at a reference age (Figure4). The rotation rotation lengths were three years for the best site, expanding to five years for the worst sites, when lengths were three years for the best site, expanding to five years for the worst sites, when there were −1 there were no other constraints. Considering a balsa tree density of 1300 trees ha , the MAI3 was 1194.8 no other constraints. Considering a balsa tree density of 300 trees ha− , the MAI was 194.8 m ha− for 3 −1 3 −1 3 −1 m ha for the best3 SI, 186.6 m ha for intermediate SI, 3and 27.71 m ha for the lowest SI. the best SI, 86.6 m ha− for intermediate SI, and 27.7 m ha− for the lowest SI.

) 300 PAI 34 -1 PAI 29

year 250 PAI 24 -1 PAI 19

ha PAI 14 3 200 MAI 34 MAI 29 MAI 24 150 MAI 19 MAI 14 100

50 Volumen increment (m increment Volumen

0 012345678910 Age (year)

FigureFigure 4. 4. RelationshipRelationship betweenbetween meanmean annualannual incrementincrement (MAI)(MAI) (dashed(dashed line)line)and andperiodic periodic annual annual incrementincrement (PAI) (PAI) curves curves (solid (solid lines) lines) for for the the volume volume incrementincrement atat didifferentfferent agesages andand SISI atat fivefive years.years. CoincidenceCoincidence of of these these two two parameters parameters can can be be considered consider toed indicateto indicate the optimumthe optimum biological biological rotation rotation age with a density of 300 trees ha 1 for the balsa plantations in the littoral region of Ecuador. The numbers age with a density of 300 trees− ha−1 for the balsa plantations in the littoral region of Ecuador. The associated with MAI and PAI correspond to the SI estimated by the height (14, 19, 24, 29, and 34 m) of numbers associated with MAI and PAI correspond to the SI estimated by the height (14, 19, 24, 29, mean dominant trees at five years. The volume was estimated with Equation (6) [38]. and 34 m) of mean dominant trees at five years. The volume was estimated with Equation (6) [39]. 4. Discussion 4. Discussion 4.1. Site Index Assessment of Height and Diameter 4.1. Site Index Assessment of Height and Diameter Comparison of the Chapman-Richards and Hossfeld models with the GADA model revealed that theComparison latter provided of the Chapman-Richards better fits and site and index Hossfeld curves models for both withHd andthe GADADBHd andmodel generated revealed polymorphicthat the latter curves. provided These better types offits curves and site are comparableindex curves with for those both obtained Hd and byDBH Cañadasd and generated et al. [36] forpolymorphicTectona; Rodr curves.íguez-Carrillo These types et of al. curves [47] are for comparJuniperusable;D withíaz-Maroto those obtained et al. [48 by] Cañadas for Quercus et al.and [37] Diforéguez-Aranda Tectona; Rodríguez-Carrillo et al. [49] for Pinus et .al. The [48] Chapman-Richards for Juniperus; Díaz-Maroto and Hossfeld et al. models [49] for presented Quercus early and asymptotesDiéguez-Aranda and greatly et al. overestimated[50] for Pinus. HThed and Chapman-RichardsDBHd at early ages. and The Hossfeld Chapman-Richards models presented models early for balsaasymptotes were used and by greatly Cañadas overestimated et al. [10] in H Ecuadord and DBH tod determineat early ages. the The SI from Chapman-Richards both height and models diameter. for Bybalsa contrast, were used the polymorphic by Cañadas et curves al. [10] obtained in Ecuador by to the determine GADA method the SI from best both described height the and growth diameter. of balsa,By contrast, especially the for polymorphic plantations curves aged between obtained one by and the three GADA years method old. Graphical best described analysis the of growth bias and of RMSEbalsa, showedespecially that for the plantations GADA model aged best between described one and the biologicalthree years parameters old. Graphical by passing analysis the of site bias index and curvesRMSE forshowed the observed that the dataGADA of H modeld and DBHbest describedd age. These the results biological are consistentparameters with by thosepassing obtained the site byindex Stankova curves and for Ditheéguez-Aranda observed data [50 of], whoHd and highlight DBHd theage. benefits These results of the GADAare consistent procedure, with which those providesobtained the by bestStankova model and fits. Diéguez-Aranda [51], who highlight the benefits of the GADA procedure, whichGräfe provides [51] observed the best a model surprisingly fits. rapid growth of balsa at a young age within a . This explainsGräfe [52] why observed balsa reaches a surprisingly its final height rapid after growth only of seven balsa years. at a Underyoung favorable age within environmental a secondary conditionsforest. This this explains was about why 20 m,balsa and reaches under unfavorableits final height conditions, after only about seven 12 m. years. The final Under growth favorable point environmental conditions this was about 20 m, and under unfavorable conditions, about 12 m. The

Forests 2019, 10, 733 11 of 16 of H and DBH was not observed in our study areas, where balsa was cultivated in plantations of the same age. According to Lamprecht [52], balsa (Ochroma lagopus (Cav. Ex Lam.) Urb) generally requires 1 average annual precipitation of between 1500 to 3000 mm year− and an average temperature of 22 to 27 ◦C. The edaphic demands for optimal growth of such forest plantations are exceptionally high. Optimal growth of balsa only occurs in deep soils of alluvial origin, with a sandy or slightly clayish texture, resulting from the weathering of rocks rich in bases. These edaphoclimatic conditions coincide with the best sites for growing balsa in the province of Los Ríos (Table1), in the Ecuadorian coastal lowlands, as mentioned above. Our data differed from those obtained by Lamprecht [52], who recorded a height of 19 m and DBH of 33 cm at the age of five years in fertile alluvial soils of the Venezuelan western llanos. 1 In Panama, heights of 7.0 m were recorded for the Soberania site (precipitation of 2226 mm year− , 1 4.0 dry months), on the Los Santos site 5.8 m (1946 mm year− , 5.2 dry months) and 3.6 m in Río Hato 1 (1107 mm year− , 6.7 dry months) for plantations aged two years [53]. These values are lower than those obtained in the present study. 1 Sites with rainfall equal or below 1000 mm year− with seven dry months (here the province of Manabí in the tropical dry forest life zone, TdF-TrF with evapotranspiration ratio of 1–2) or precipitation 1 of 3019 mm year− and no dry months (province of Cotopaxi, Twf-TrF with a evapotranspiration ratio 0.2–0.5) were limiting conditions for balsa growth, indicated by Hd = 15.3 m, DBHd = 15.6 cm to Hd = 20.0 m, DBHd = 21.4 cm at five years. This is consistent with the observations made by Butterfield [54], Dalling et al. [55], Pearson et al. [56], Healy et al. [57], van Breugel et al. [58], and Azambuja et al. [59], who emphasized that (micro-) variations in water and soils locally affect the tree growth and survival of balsa. Early successional species such as balsa generally show exceptional growth: Their crowns suppress weeds [54] and quickly improve the environmental conditions [60]. Balsa is characterized by high survival rates [61]. Nevertheless, de-Miguel et al. [19] observed high mortality in balsa, which affected by suboptimal environmental conditions in Bolivia and is considered a consequence of manual weed control. Such occurrences were not observed in the balsa plantations in our study region, as 61.5% of the weed control is carried out with chemicals in this part of Ecuador. Lamprecht [52] mentioned that no economic damage or diseases have been observed in plantations of O. lagopus, another species of balsa grown in tropical regions. In this study, efforts have been made to develop god fitting balsa site index models for the coastal lowlands of Ecuador. However, these models can be improved in relation to dendro-ecological resolution, developing individual growth models used in other studies [13,62]. The inclusion of additional variables such as position, size of specific trees and spatial distribution could help to improve the understanding of the stand growth and production [13].

4.2. Tree Volume Assessment Volume estimation plays a major role in productive forests. This is the first report of balsa volume models. In general, the Newnham model (Equation (13)) consistently provided adequate volume estimates, as demonstrated by the fitting statistics for balsa, indicated by the low MSE and AIC and 2 high R Adj value. Newnham [43] proposed use of the Newnham model to estimate the volumes for Pinus banksiana Lamb., Dougl., Picea glauca (Moench) and tremuloides Michx in Alberta, Canada. In Ecuador, Cañadas et al. [36] used the Newnham model in a comparative study to describe the volume of Tectona grandis L. (teak) under agroforestry systems, and the model also provided the best fit to the data. This was also found by Hernández-Ramos [63] for urophylla S.T.Blake. The balsa volume equation based on the Newnham formula (Equation (13)) overestimated smaller trees (0.34 m3), because parameter a amounted to 0.34 (i.e., the smallest tree (DBH = 5 cm) would already have a volume of 0.34 m3). Forests 2019, 10, 733 12 of 16

However, to date, the commercial volumes have only been determined by the simple, but less accurate, volume model, predicting tree volume as a function of DBH, height, and absolute form factor of 0.7 [64–67].

4.3. Mean Annual Increment in Volume We chose to use the Schumacher-Hall (allometric) (Equation (6)) formula to calculate the volume and to estimate MAI and PAI, due to the better estimation of small tree dimensions. MAI and PAI coincided at three years of the balsa plantation growth as optimal biological rotation in the best site conditions. Therefore, the maximum rotation length increased rapidly with decreasing SI. These results are very different from those obtained by de-Miguel et al. [19], who proposed that the duration of the maximum rotation of balsa plantations in Bolivia would be one year if the size of trees and economic aspects are not considered. In the present study, the results indicated a three-year rotation for the best SI and five years for the SI. Harvesting at that age would take advantage of the low specific gravity of the young wood [68]. However, these data differ from those obtained by Longwood [69] who suggested rotation lengths of between four to six years for balsa plantations. Webb [70] suggested rotations of between seven to eight years. González-Osorio et al. [71] and Midgley et al. [4] determined optimal rotation lengths of between four to eight years. All the aforementioned researchers did not describe the method applied to determine the rotation age. However, de-Miguel et al. [19] assumed a rotation of five years in a study conducted in Bolivia using an individual-tree innovative approach. Nevertheless, beyond technical forestry concerns, in the tropical lowland regions of Ecuador balsa is commercialized when a DBH of 18 cm or more is reached. This is due to the traders’ prices for whole trees (10 to 15 US $ per tree). However, industry demands larger DBH (33–40 cm), doubling the tree value [71], and such diameters can be reached in the best SI at three years of age (Figure2B). 3 1 The maximum variations in MAI of 202, 87, and 28 m ha− for good, medium, and poor sites, respectively, demonstrated that balsa behaves as a typical pioneer species and is highly sensitive to site conditions [4]. Wycherley and Mitchell [72] concluded that MAI followed a decreasing trend of this forest parameter at plantation establishment. By contrast, we have found that the maximum MAI was reached after two years for the best SI, four years for intermediate SI, and five years for the worst SI. For the best SI, the MAI observed in the present study cannot be compared in quantity nor in rotation 3 1 lengths with those obtained by Webb [70], who measured MAI in volume between 17 and 30 m ha− 1 year− in tropical regions at ages of seven and eight years old. However, plantation densities were not provided. Nevertheless, Howcroft [73] and Midgley et al. [4] mentioned that stands older than five to seven years were characterized by poor growth and wood quality. In Bolivia, de-Miguel et al. [19] predicted 3 1 1 a mean annual commercial volume increment of 5.9, 10.4, and 12.9 m ha− year− in five-year-old plantations, for poor, medium, and good sites, respectively; plantation densities were not presented because of the high mortality recorded.

5. Conclusions In summary, forest models describe how trees grow and how forest structures are modified over time. The site index models for DBH and H, and volume and MAI, obtained in the present study must be validated with an independent sample for comparison of these forest parameters. Such validation could contribute to enable reasonable predictions to be made about balsa tree growth and stand development in the coastal lowlands of Ecuador. Moreover, balsa is an example of a native tree whose socio-economic and ecological potential is not yet fully known or exploited. Balsa is a pioneer species that thrives on abandoned land and is maintained with minimal input of labor, usually with a high survival rate and triggering forest succession. Despite the multiple attributes of this native species, it has unfortunately not yet been promoted by the Ecuadorian state program. However, the current environmental challenges associated with climate variation or change, deterioration of ecosystem services, and decline in biodiversity require several solutions. Forests 2019, 10, 733 13 of 16

These can be obtained through reforestation with fast-growing native species with high potential of production, while at the same time recovering degraded areas.

Author Contributions: Á.C.-L., D.R.-L. and G.M.-M. conceived and designed the experiments, collected the data, and wrote the first draft; Á.C.-L., J.J.V.-H. and C.W. expanded the statistical analyses and M.S.-S. the argumentation lines; C.W. and M.S.-S. carried out a detailed revision of the paper. Funding: This research received no external funding. Acknowledgments: We thank the Director of the Portoviejo Experimental Research Station (EEP) of the National Institute of Agricultural Research (INIAP) and the INIAP General Director for providing the necessary logistics and resources in order to carry out this project. Conflicts of Interest: The authors declare no conflict of interest.

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